Center Controller reported assigning an altitude that was below the minimum IFR altitude to an aircraft approaching an airport. The minimum IFR altitudes in the local area had recently changed.

Narrative

Aircraft X was inbound to the DLS airport from the northwest. The aircraft was leveled at 11;000 and asked for a lower altitude. I waited until he was at a lower MIA and gave them discretion to 8;000. Our MIA's changed less than a month ago and I didn't realize there was a thin stretch of 9;000 between the lower MIA's. I was working two sectors with multiple frequencies and also alternating between frequency sites. At that point; I was offered a break but I was still fairly busy so I asked the other controller to sit with me for few minutes on my D-side. As I was starting to brief; the MSAW alert started flashing to indicate the low altitude alert. I assigned the aircraft a climb back to 9;000. There was really no way to safely keep him in the 8;000 MIA once I saw the flash. We have been short staffed and I just wish had I asked for a D-side earlier so I can get proper support and extra pair of eyes to help with sector management. That also would've helped traffic/terrain re-evaluation once I started the aircraft's descent.